Upon production of a semiconductor device, there is generally an intermediate layer between an Si substrate and a resist. In the case where a MOS transistor is produced, for example, on patterning a resist for forming an element separating layer as the first step, an oxide film has been formed under the resist. Accordingly, as shown in FIG. 1A, in the case where a resist layer 2 (positive type in this example) is formed on an Si substrate 1, intermediate layers 3a, 3b and 3c of SiO.sub.2 and Si.sub.3 N.sub.4 has been formed on the Si substrate 1.
In the case where the intermediate layer 3a does not reflect or transmit light but does completely absorb light as in FIG. 1A, the intermediate layer 3a does not give any influence on the shape of the resist layer 2 as an upper layer after patterning, i.e., the shape of a resist pattern 2a as shown in FIG. 1B.
On the other hand, in the case of the intermediate layers 3b and 3c reflecting light, the reflected light returns to the resist layer 2 to interfere with the incident light, i.e., the so-called standing wave effect occurs. Because of the presence of the intermediate layer 3b (or 3c), interference of a mixture of the optical constants n and k and the film thickness of the intermediate layer 3b (or 3c) occurs, as different from the simple standing wave of only the Si substrate 1 and the resist layer 2. The optical constant n is the real part of the reflective index, i.e., the ratio of the light velocity in vacuo and the light velocity in the substance at issue. The optical constant k is the imaginary part of the reflective index, which is determined by the light absorption coefficient .alpha. of the substance at issue (represented by 4.pi..alpha./.lambda. where .lambda. represents the wavelength).
Accordingly, as shown by B in FIG. 1B, a broad slope called "tailing" is formed at the boundary between the resist pattern 2b formed by patterning by exposure and development and the intermediate layer 3b under the resist pattern, and also as shown by C in FIG. 1B, a scooping called "undercut" is formed at the boundary between the resist pattern 2c and the intermediate layer 3c under the resist pattern.
When the tailing occurs, the tailing part functions as a mask on etching the intermediate layer 3b using the resist pattern 2b as a mask, and the intermediate layer 3b positioned under the tailing part is not sufficiently etched. As a result, the line width under the resist after etching is thickened.
On the other hand, when the undercut occurs, stress concentration occurs at the undercut part by the surface tension on the development of the resist pattern 2c, and the resist pattern 2c is collapsed as in the worst case. Even when the undercut does not proceed to bring about the collapse of the resist pattern, etching at the undercut part excessively proceeds.
When the tailing or the undercut occurs uniformly within the surface of the Si substrate 1, it is possible to determine the line width of the resist taking the change of the line width on etching into consideration, but in the practical device, the tailing or the undercut does not occur uniformly.
The intermediate layers 3b and 3c is formed by a film forming process, such as the CVD process, the spattering process and the spin coating process. An apparatus for producing a semiconductor device conducting such film forming processed is recently improved in its performance, and the uniformity of the thickness and the optical characteristics of the film produced by the processes is greatly improved than those in former times.
However, a slight fluctuation (unevenness) still remains even in the film forming process of such an apparatus for producing a semiconductor device, and the unevenness in the film thickness and the optical characteristics of the film cannot be completely removed.
In the case of a structure comprising a resist layer, an SiN layer (intermediate layer) and an Si substrate in this order, for example, when the thickness of the SiN layer changes to as small as 0.02 .mu.m, the shape of the resist pattern obtained by patterning changes from the tailing to the undercut. Accordingly, due to the slight fluctuation of the thickness of the SiN layer (intermediate layer), the resist pattern is collapsed or a bridge (resist remains in a part which is planned as the resist should not remain) is produced in a space of the pattern.
Results of the simulation when the tailing occurs in the resist pattern are shown in FIGS. 2A-1 and 2A-2, and results of the simulation where the undercut occurs are shown in FIGS. 2B-1 and 2B-2. These figures of simulation show examples of an Si substrate, an SiN layer (intermediate layer) and the resist layer in this order from the bottom, where a positive resist is used as the resist. Therefore, the part that remains as horizontally protrudes (in a convex state) in FIGS. 2A-2 and 2B-2 is an unexposed part where light is not irradiated since the resist is a positive type.
In the case of the tailing mode in FIGS. 2A-1 and 2A-2, the light absorption energy at the interface between the resist and the SiN layer (intermediate layer) becomes small as shown in FIG. 2A-1. Therefore, in the PEB (post exposure bake) process where an acid is produced by baking after exposure to change the development rate, since the amount of an acid produced at the interface between the resist and the SiN layer (intermediate layer) becomes small, the dissolution rate is decreased, and the bottom of the resist remains as tailing shown in FIG. 2A-2.
In the case of undercut, on the other hand, since the light absorption energy at the interface between the resist and the SiN layer (intermediate layer) becomes the maximum, a large amount of an acid is generated by the PEB process to raise the dissolution rate, and thus the undercut occurs.
In a simple model composed of a substrate and a resist formed directly on the substrate, the shape of the resist pattern can be controlled by adjusting the film thickness of the resist.
However, in the case where the optical constants n.sub.1 and k.sub.1 of the intermediate layer formed under the resist layer is larger than the optical constants n.sub.2 and k.sub.2 of the resist layer, the shape of the resist pattern obtained by pattering is predominantly influenced by the film thickness of the intermediate layer. Therefore, the film thickness of the intermediate layer positioned under the resist film must be optimized to stably obtain a resist pattern having a desired shape.
Under the circumstances, it has been conventionally practiced that in order to conduct the optimization of the film thickness of the intermediate layer, plural samples having film thickness values different from each other are prepared, and an exposure experiment is actually conducted to determine the optimum film thickness.
However, this method involves a disadvantage in that large amounts of time and cost are required to prepare the plural samples.